Opossums were introduced to the Western US, where they became an invasive species (although not to the degree of the Common Brushtail Possum in NZ)
Regarding the subject of introduced species that get away with becoming invasive due to their charismatic nature:
Gray-headed Swamphens (which, depending on the taxonomy used, may or may not be the same species as the popular Pukeko of Australasia) have escaped from private collections in Florida. They may become considered charismatic to the point of people letting them invade. I discussed invasive birds with a former keeper from the Bird Kingdom aviary on the comments section of his YouTube video, and I noted that the Gray-headed Swamphen is one species that we still have time to remove, unlike so many others that are unstoppable at this point, such as the House Sparrow and European Starling. In his reply, he stated that “At first I was like, "Aw, Swamphens are cute!" but that's the problem we're talking about. They don't stop being cute while they outcompete every native species!” This raises a question about whether the eradication of this species may be delayed or worse, never executed at all, due to human cultural attitudes.
On a related note, in the same discussion, I brought up how feral pigeons are becoming popular in North America. For example, there’s the Audubon article about our “misguided hatred of pigeons”, the point being that many people are reluctant to coexist with wildlife in urban areas. I do think that people should be more accepting of wild animals in populated areas, but people should be subsidizing native species, and the Rock Pigeon is not one of them in North America, even though Band-tailed Pigeons, Mourning Doves, White-winged Doves, etc. are fine, however. Then there’s the book A Pocket Guide to Pigeon Watching, which portrayed Rock Pigeons as the most misunderstood bird. It was authored and illustrated by someone who is otherwise very environmentally literate: the nature cartoonist Rosemary Mosco, best known for Birding is my Favorite Video Game. And what is even worse? It was advertised on the Cornell Lab’s website, of all places, and it was given a seal of approval by the otherwise serious and professional David Allen Sibley, of all people! I must note that the wild form of Rock Pigeons are perfectly fine in Europe where they are from, but even there, the feral variety threatens its wild ancestor.
Therefore, my hot take is that Rock Pigeons (specifically feral ones) are overrated now.